/*
 * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
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 *
 *
 *
 *
 *
 *
 *
 */

package java.lang;

import java.lang.annotation.Native;
import java.math.*;


/**
 * The {@code Long} class wraps a value of the primitive type {@code
 * long} in an object. An object of type {@code Long} contains a
 * single field whose type is {@code long}.
 *
 * <p> In addition, this class provides several methods for converting
 * a {@code long} to a {@code String} and a {@code String} to a {@code
 * long}, as well as other constants and methods useful when dealing
 * with a {@code long}.
 *
 * <p>Implementation note: The implementations of the "bit twiddling"
 * methods (such as {@link #highestOneBit(long) highestOneBit} and
 * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
 * based on material from Henry S. Warren, Jr.'s <i>Hacker's
 * Delight</i>, (Addison Wesley, 2002).
 *
 * @author Lee Boynton
 * @author Arthur van Hoff
 * @author Josh Bloch
 * @author Joseph D. Darcy
 * @since JDK1.0
 */
public final class Long extends Number implements Comparable<Long> {

  /**
   * A constant holding the minimum value a {@code long} can
   * have, -2<sup>63</sup>.
   */
  @Native
  public static final long MIN_VALUE = 0x8000000000000000L;

  /**
   * A constant holding the maximum value a {@code long} can
   * have, 2<sup>63</sup>-1.
   */
  @Native
  public static final long MAX_VALUE = 0x7fffffffffffffffL;

  /**
   * The {@code Class} instance representing the primitive type
   * {@code long}.
   *
   * @since JDK1.1
   */
  @SuppressWarnings("unchecked")
  public static final Class<Long> TYPE = (Class<Long>) Class.getPrimitiveClass("long");

  /**
   * Returns a string representation of the first argument in the
   * radix specified by the second argument.
   *
   * <p>If the radix is smaller than {@code Character.MIN_RADIX}
   * or larger than {@code Character.MAX_RADIX}, then the radix
   * {@code 10} is used instead.
   *
   * <p>If the first argument is negative, the first element of the
   * result is the ASCII minus sign {@code '-'}
   * ({@code '\u005Cu002d'}). If the first argument is not
   * negative, no sign character appears in the result.
   *
   * <p>The remaining characters of the result represent the magnitude
   * of the first argument. If the magnitude is zero, it is
   * represented by a single zero character {@code '0'}
   * ({@code '\u005Cu0030'}); otherwise, the first character of
   * the representation of the magnitude will not be the zero
   * character.  The following ASCII characters are used as digits:
   *
   * <blockquote>
   * {@code 0123456789abcdefghijklmnopqrstuvwxyz}
   * </blockquote>
   *
   * These are {@code '\u005Cu0030'} through
   * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
   * {@code '\u005Cu007a'}. If {@code radix} is
   * <var>N</var>, then the first <var>N</var> of these characters
   * are used as radix-<var>N</var> digits in the order shown. Thus,
   * the digits for hexadecimal (radix 16) are
   * {@code 0123456789abcdef}. If uppercase letters are
   * desired, the {@link java.lang.String#toUpperCase()} method may
   * be called on the result:
   *
   * <blockquote>
   * {@code Long.toString(n, 16).toUpperCase()}
   * </blockquote>
   *
   * @param i a {@code long} to be converted to a string.
   * @param radix the radix to use in the string representation.
   * @return a string representation of the argument in the specified radix.
   * @see java.lang.Character#MAX_RADIX
   * @see java.lang.Character#MIN_RADIX
   */
  public static String toString(long i, int radix) {
    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
      radix = 10;
    }
    if (radix == 10) {
      return toString(i);
    }
    char[] buf = new char[65];
    int charPos = 64;
    boolean negative = (i < 0);

    if (!negative) {
      i = -i;
    }

    while (i <= -radix) {
      buf[charPos--] = Integer.digits[(int) (-(i % radix))];
      i = i / radix;
    }
    buf[charPos] = Integer.digits[(int) (-i)];

    if (negative) {
      buf[--charPos] = '-';
    }

    return new String(buf, charPos, (65 - charPos));
  }

  /**
   * Returns a string representation of the first argument as an
   * unsigned integer value in the radix specified by the second
   * argument.
   *
   * <p>If the radix is smaller than {@code Character.MIN_RADIX}
   * or larger than {@code Character.MAX_RADIX}, then the radix
   * {@code 10} is used instead.
   *
   * <p>Note that since the first argument is treated as an unsigned
   * value, no leading sign character is printed.
   *
   * <p>If the magnitude is zero, it is represented by a single zero
   * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
   * the first character of the representation of the magnitude will
   * not be the zero character.
   *
   * <p>The behavior of radixes and the characters used as digits
   * are the same as {@link #toString(long, int) toString}.
   *
   * @param i an integer to be converted to an unsigned string.
   * @param radix the radix to use in the string representation.
   * @return an unsigned string representation of the argument in the specified radix.
   * @see #toString(long, int)
   * @since 1.8
   */
  public static String toUnsignedString(long i, int radix) {
    if (i >= 0) {
      return toString(i, radix);
    } else {
      switch (radix) {
        case 2:
          return toBinaryString(i);

        case 4:
          return toUnsignedString0(i, 2);

        case 8:
          return toOctalString(i);

        case 10:
                /*
                 * We can get the effect of an unsigned division by 10
                 * on a long value by first shifting right, yielding a
                 * positive value, and then dividing by 5.  This
                 * allows the last digit and preceding digits to be
                 * isolated more quickly than by an initial conversion
                 * to BigInteger.
                 */
          long quot = (i >>> 1) / 5;
          long rem = i - quot * 10;
          return toString(quot) + rem;

        case 16:
          return toHexString(i);

        case 32:
          return toUnsignedString0(i, 5);

        default:
          return toUnsignedBigInteger(i).toString(radix);
      }
    }
  }

  /**
   * Return a BigInteger equal to the unsigned value of the
   * argument.
   */
  private static BigInteger toUnsignedBigInteger(long i) {
    if (i >= 0L) {
      return BigInteger.valueOf(i);
    } else {
      int upper = (int) (i >>> 32);
      int lower = (int) i;

      // return (upper << 32) + lower
      return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
          add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
    }
  }

  /**
   * Returns a string representation of the {@code long}
   * argument as an unsigned integer in base&nbsp;16.
   *
   * <p>The unsigned {@code long} value is the argument plus
   * 2<sup>64</sup> if the argument is negative; otherwise, it is
   * equal to the argument.  This value is converted to a string of
   * ASCII digits in hexadecimal (base&nbsp;16) with no extra
   * leading {@code 0}s.
   *
   * <p>The value of the argument can be recovered from the returned
   * string {@code s} by calling {@link
   * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
   * 16)}.
   *
   * <p>If the unsigned magnitude is zero, it is represented by a
   * single zero character {@code '0'} ({@code '\u005Cu0030'});
   * otherwise, the first character of the representation of the
   * unsigned magnitude will not be the zero character. The
   * following characters are used as hexadecimal digits:
   *
   * <blockquote>
   * {@code 0123456789abcdef}
   * </blockquote>
   *
   * These are the characters {@code '\u005Cu0030'} through
   * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
   * {@code '\u005Cu0066'}.  If uppercase letters are desired,
   * the {@link java.lang.String#toUpperCase()} method may be called
   * on the result:
   *
   * <blockquote>
   * {@code Long.toHexString(n).toUpperCase()}
   * </blockquote>
   *
   * @param i a {@code long} to be converted to a string.
   * @return the string representation of the unsigned {@code long} value represented by the
   * argument in hexadecimal (base&nbsp;16).
   * @see #parseUnsignedLong(String, int)
   * @see #toUnsignedString(long, int)
   * @since JDK 1.0.2
   */
  public static String toHexString(long i) {
    return toUnsignedString0(i, 4);
  }

  /**
   * Returns a string representation of the {@code long}
   * argument as an unsigned integer in base&nbsp;8.
   *
   * <p>The unsigned {@code long} value is the argument plus
   * 2<sup>64</sup> if the argument is negative; otherwise, it is
   * equal to the argument.  This value is converted to a string of
   * ASCII digits in octal (base&nbsp;8) with no extra leading
   * {@code 0}s.
   *
   * <p>The value of the argument can be recovered from the returned
   * string {@code s} by calling {@link
   * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
   * 8)}.
   *
   * <p>If the unsigned magnitude is zero, it is represented by a
   * single zero character {@code '0'} ({@code '\u005Cu0030'});
   * otherwise, the first character of the representation of the
   * unsigned magnitude will not be the zero character. The
   * following characters are used as octal digits:
   *
   * <blockquote>
   * {@code 01234567}
   * </blockquote>
   *
   * These are the characters {@code '\u005Cu0030'} through
   * {@code '\u005Cu0037'}.
   *
   * @param i a {@code long} to be converted to a string.
   * @return the string representation of the unsigned {@code long} value represented by the
   * argument in octal (base&nbsp;8).
   * @see #parseUnsignedLong(String, int)
   * @see #toUnsignedString(long, int)
   * @since JDK 1.0.2
   */
  public static String toOctalString(long i) {
    return toUnsignedString0(i, 3);
  }

  /**
   * Returns a string representation of the {@code long}
   * argument as an unsigned integer in base&nbsp;2.
   *
   * <p>The unsigned {@code long} value is the argument plus
   * 2<sup>64</sup> if the argument is negative; otherwise, it is
   * equal to the argument.  This value is converted to a string of
   * ASCII digits in binary (base&nbsp;2) with no extra leading
   * {@code 0}s.
   *
   * <p>The value of the argument can be recovered from the returned
   * string {@code s} by calling {@link
   * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
   * 2)}.
   *
   * <p>If the unsigned magnitude is zero, it is represented by a
   * single zero character {@code '0'} ({@code '\u005Cu0030'});
   * otherwise, the first character of the representation of the
   * unsigned magnitude will not be the zero character. The
   * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
   * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
   *
   * @param i a {@code long} to be converted to a string.
   * @return the string representation of the unsigned {@code long} value represented by the
   * argument in binary (base&nbsp;2).
   * @see #parseUnsignedLong(String, int)
   * @see #toUnsignedString(long, int)
   * @since JDK 1.0.2
   */
  public static String toBinaryString(long i) {
    return toUnsignedString0(i, 1);
  }

  /**
   * Format a long (treated as unsigned) into a String.
   *
   * @param val the value to format
   * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
   */
  static String toUnsignedString0(long val, int shift) {
    // assert shift > 0 && shift <=5 : "Illegal shift value";
    int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
    int chars = Math.max(((mag + (shift - 1)) / shift), 1);
    char[] buf = new char[chars];

    formatUnsignedLong(val, shift, buf, 0, chars);
    return new String(buf, true);
  }

  /**
   * Format a long (treated as unsigned) into a character buffer.
   *
   * @param val the unsigned long to format
   * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
   * @param buf the character buffer to write to
   * @param offset the offset in the destination buffer to start at
   * @param len the number of characters to write
   * @return the lowest character location used
   */
  static int formatUnsignedLong(long val, int shift, char[] buf, int offset, int len) {
    int charPos = len;
    int radix = 1 << shift;
    int mask = radix - 1;
    do {
      buf[offset + --charPos] = Integer.digits[((int) val) & mask];
      val >>>= shift;
    } while (val != 0 && charPos > 0);

    return charPos;
  }

  /**
   * Returns a {@code String} object representing the specified
   * {@code long}.  The argument is converted to signed decimal
   * representation and returned as a string, exactly as if the
   * argument and the radix 10 were given as arguments to the {@link
   * #toString(long, int)} method.
   *
   * @param i a {@code long} to be converted.
   * @return a string representation of the argument in base&nbsp;10.
   */
  public static String toString(long i) {
    if (i == Long.MIN_VALUE) {
      return "-9223372036854775808";
    }
    int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
    char[] buf = new char[size];
    getChars(i, size, buf);
    return new String(buf, true);
  }

  /**
   * Returns a string representation of the argument as an unsigned
   * decimal value.
   *
   * The argument is converted to unsigned decimal representation
   * and returned as a string exactly as if the argument and radix
   * 10 were given as arguments to the {@link #toUnsignedString(long,
   * int)} method.
   *
   * @param i an integer to be converted to an unsigned string.
   * @return an unsigned string representation of the argument.
   * @see #toUnsignedString(long, int)
   * @since 1.8
   */
  public static String toUnsignedString(long i) {
    return toUnsignedString(i, 10);
  }

  /**
   * Places characters representing the integer i into the
   * character array buf. The characters are placed into
   * the buffer backwards starting with the least significant
   * digit at the specified index (exclusive), and working
   * backwards from there.
   *
   * Will fail if i == Long.MIN_VALUE
   */
  static void getChars(long i, int index, char[] buf) {
    long q;
    int r;
    int charPos = index;
    char sign = 0;

    if (i < 0) {
      sign = '-';
      i = -i;
    }

    // Get 2 digits/iteration using longs until quotient fits into an int
    while (i > Integer.MAX_VALUE) {
      q = i / 100;
      // really: r = i - (q * 100);
      r = (int) (i - ((q << 6) + (q << 5) + (q << 2)));
      i = q;
      buf[--charPos] = Integer.DigitOnes[r];
      buf[--charPos] = Integer.DigitTens[r];
    }

    // Get 2 digits/iteration using ints
    int q2;
    int i2 = (int) i;
    while (i2 >= 65536) {
      q2 = i2 / 100;
      // really: r = i2 - (q * 100);
      r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
      i2 = q2;
      buf[--charPos] = Integer.DigitOnes[r];
      buf[--charPos] = Integer.DigitTens[r];
    }

    // Fall thru to fast mode for smaller numbers
    // assert(i2 <= 65536, i2);
    for (; ; ) {
      q2 = (i2 * 52429) >>> (16 + 3);
      r = i2 - ((q2 << 3) + (q2 << 1));  // r = i2-(q2*10) ...
      buf[--charPos] = Integer.digits[r];
      i2 = q2;
      if (i2 == 0) {
        break;
      }
    }
    if (sign != 0) {
      buf[--charPos] = sign;
    }
  }

  // Requires positive x
  static int stringSize(long x) {
    long p = 10;
    for (int i = 1; i < 19; i++) {
      if (x < p) {
        return i;
      }
      p = 10 * p;
    }
    return 19;
  }

  /**
   * Parses the string argument as a signed {@code long} in the
   * radix specified by the second argument. The characters in the
   * string must all be digits of the specified radix (as determined
   * by whether {@link java.lang.Character#digit(char, int)} returns
   * a nonnegative value), except that the first character may be an
   * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
   * indicate a negative value or an ASCII plus sign {@code '+'}
   * ({@code '\u005Cu002B'}) to indicate a positive value. The
   * resulting {@code long} value is returned.
   *
   * <p>Note that neither the character {@code L}
   * ({@code '\u005Cu004C'}) nor {@code l}
   * ({@code '\u005Cu006C'}) is permitted to appear at the end
   * of the string as a type indicator, as would be permitted in
   * Java programming language source code - except that either
   * {@code L} or {@code l} may appear as a digit for a
   * radix greater than or equal to 22.
   *
   * <p>An exception of type {@code NumberFormatException} is
   * thrown if any of the following situations occurs:
   * <ul>
   *
   * <li>The first argument is {@code null} or is a string of
   * length zero.
   *
   * <li>The {@code radix} is either smaller than {@link
   * java.lang.Character#MIN_RADIX} or larger than {@link
   * java.lang.Character#MAX_RADIX}.
   *
   * <li>Any character of the string is not a digit of the specified
   * radix, except that the first character may be a minus sign
   * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
   * '+'} ({@code '\u005Cu002B'}) provided that the string is
   * longer than length 1.
   *
   * <li>The value represented by the string is not a value of type
   * {@code long}.
   * </ul>
   *
   * <p>Examples:
   * <blockquote><pre>
   * parseLong("0", 10) returns 0L
   * parseLong("473", 10) returns 473L
   * parseLong("+42", 10) returns 42L
   * parseLong("-0", 10) returns 0L
   * parseLong("-FF", 16) returns -255L
   * parseLong("1100110", 2) returns 102L
   * parseLong("99", 8) throws a NumberFormatException
   * parseLong("Hazelnut", 10) throws a NumberFormatException
   * parseLong("Hazelnut", 36) returns 1356099454469L
   * </pre></blockquote>
   *
   * @param s the {@code String} containing the {@code long} representation to be parsed.
   * @param radix the radix to be used while parsing {@code s}.
   * @return the {@code long} represented by the string argument in the specified radix.
   * @throws NumberFormatException if the string does not contain a parsable {@code long}.
   */
  public static long parseLong(String s, int radix)
      throws NumberFormatException {
    if (s == null) {
      throw new NumberFormatException("null");
    }

    if (radix < Character.MIN_RADIX) {
      throw new NumberFormatException("radix " + radix +
          " less than Character.MIN_RADIX");
    }
    if (radix > Character.MAX_RADIX) {
      throw new NumberFormatException("radix " + radix +
          " greater than Character.MAX_RADIX");
    }

    long result = 0;
    boolean negative = false;
    int i = 0, len = s.length();
    long limit = -Long.MAX_VALUE;
    long multmin;
    int digit;

    if (len > 0) {
      char firstChar = s.charAt(0);
      if (firstChar < '0') { // Possible leading "+" or "-"
        if (firstChar == '-') {
          negative = true;
          limit = Long.MIN_VALUE;
        } else if (firstChar != '+') {
          throw NumberFormatException.forInputString(s);
        }

        if (len == 1) // Cannot have lone "+" or "-"
        {
          throw NumberFormatException.forInputString(s);
        }
        i++;
      }
      multmin = limit / radix;
      while (i < len) {
        // Accumulating negatively avoids surprises near MAX_VALUE
        digit = Character.digit(s.charAt(i++), radix);
        if (digit < 0) {
          throw NumberFormatException.forInputString(s);
        }
        if (result < multmin) {
          throw NumberFormatException.forInputString(s);
        }
        result *= radix;
        if (result < limit + digit) {
          throw NumberFormatException.forInputString(s);
        }
        result -= digit;
      }
    } else {
      throw NumberFormatException.forInputString(s);
    }
    return negative ? result : -result;
  }

  /**
   * Parses the string argument as a signed decimal {@code long}.
   * The characters in the string must all be decimal digits, except
   * that the first character may be an ASCII minus sign {@code '-'}
   * ({@code \u005Cu002D'}) to indicate a negative value or an
   * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
   * indicate a positive value. The resulting {@code long} value is
   * returned, exactly as if the argument and the radix {@code 10}
   * were given as arguments to the {@link
   * #parseLong(java.lang.String, int)} method.
   *
   * <p>Note that neither the character {@code L}
   * ({@code '\u005Cu004C'}) nor {@code l}
   * ({@code '\u005Cu006C'}) is permitted to appear at the end
   * of the string as a type indicator, as would be permitted in
   * Java programming language source code.
   *
   * @param s a {@code String} containing the {@code long} representation to be parsed
   * @return the {@code long} represented by the argument in decimal.
   * @throws NumberFormatException if the string does not contain a parsable {@code long}.
   */
  public static long parseLong(String s) throws NumberFormatException {
    return parseLong(s, 10);
  }

  /**
   * Parses the string argument as an unsigned {@code long} in the
   * radix specified by the second argument.  An unsigned integer
   * maps the values usually associated with negative numbers to
   * positive numbers larger than {@code MAX_VALUE}.
   *
   * The characters in the string must all be digits of the
   * specified radix (as determined by whether {@link
   * java.lang.Character#digit(char, int)} returns a nonnegative
   * value), except that the first character may be an ASCII plus
   * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
   * integer value is returned.
   *
   * <p>An exception of type {@code NumberFormatException} is
   * thrown if any of the following situations occurs:
   * <ul>
   * <li>The first argument is {@code null} or is a string of
   * length zero.
   *
   * <li>The radix is either smaller than
   * {@link java.lang.Character#MIN_RADIX} or
   * larger than {@link java.lang.Character#MAX_RADIX}.
   *
   * <li>Any character of the string is not a digit of the specified
   * radix, except that the first character may be a plus sign
   * {@code '+'} ({@code '\u005Cu002B'}) provided that the
   * string is longer than length 1.
   *
   * <li>The value represented by the string is larger than the
   * largest unsigned {@code long}, 2<sup>64</sup>-1.
   *
   * </ul>
   *
   * @param s the {@code String} containing the unsigned integer representation to be parsed
   * @param radix the radix to be used while parsing {@code s}.
   * @return the unsigned {@code long} represented by the string argument in the specified radix.
   * @throws NumberFormatException if the {@code String} does not contain a parsable {@code long}.
   * @since 1.8
   */
  public static long parseUnsignedLong(String s, int radix)
      throws NumberFormatException {
    if (s == null) {
      throw new NumberFormatException("null");
    }

    int len = s.length();
    if (len > 0) {
      char firstChar = s.charAt(0);
      if (firstChar == '-') {
        throw new
            NumberFormatException(String.format("Illegal leading minus sign " +
            "on unsigned string %s.", s));
      } else {
        if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
            (radix == 10 && len <= 18)) { // Long.MAX_VALUE in base 10 is 19 digits
          return parseLong(s, radix);
        }

        // No need for range checks on len due to testing above.
        long first = parseLong(s.substring(0, len - 1), radix);
        int second = Character.digit(s.charAt(len - 1), radix);
        if (second < 0) {
          throw new NumberFormatException("Bad digit at end of " + s);
        }
        long result = first * radix + second;
        if (compareUnsigned(result, first) < 0) {
                    /*
                     * The maximum unsigned value, (2^64)-1, takes at
                     * most one more digit to represent than the
                     * maximum signed value, (2^63)-1.  Therefore,
                     * parsing (len - 1) digits will be appropriately
                     * in-range of the signed parsing.  In other
                     * words, if parsing (len -1) digits overflows
                     * signed parsing, parsing len digits will
                     * certainly overflow unsigned parsing.
                     *
                     * The compareUnsigned check above catches
                     * situations where an unsigned overflow occurs
                     * incorporating the contribution of the final
                     * digit.
                     */
          throw new NumberFormatException(String.format("String value %s exceeds " +
              "range of unsigned long.", s));
        }
        return result;
      }
    } else {
      throw NumberFormatException.forInputString(s);
    }
  }

  /**
   * Parses the string argument as an unsigned decimal {@code long}. The
   * characters in the string must all be decimal digits, except
   * that the first character may be an an ASCII plus sign {@code
   * '+'} ({@code '\u005Cu002B'}). The resulting integer value
   * is returned, exactly as if the argument and the radix 10 were
   * given as arguments to the {@link
   * #parseUnsignedLong(java.lang.String, int)} method.
   *
   * @param s a {@code String} containing the unsigned {@code long} representation to be parsed
   * @return the unsigned {@code long} value represented by the decimal string argument
   * @throws NumberFormatException if the string does not contain a parsable unsigned integer.
   * @since 1.8
   */
  public static long parseUnsignedLong(String s) throws NumberFormatException {
    return parseUnsignedLong(s, 10);
  }

  /**
   * Returns a {@code Long} object holding the value
   * extracted from the specified {@code String} when parsed
   * with the radix given by the second argument.  The first
   * argument is interpreted as representing a signed
   * {@code long} in the radix specified by the second
   * argument, exactly as if the arguments were given to the {@link
   * #parseLong(java.lang.String, int)} method. The result is a
   * {@code Long} object that represents the {@code long}
   * value specified by the string.
   *
   * <p>In other words, this method returns a {@code Long} object equal
   * to the value of:
   *
   * <blockquote>
   * {@code new Long(Long.parseLong(s, radix))}
   * </blockquote>
   *
   * @param s the string to be parsed
   * @param radix the radix to be used in interpreting {@code s}
   * @return a {@code Long} object holding the value represented by the string argument in the
   * specified radix.
   * @throws NumberFormatException If the {@code String} does not contain a parsable {@code long}.
   */
  public static Long valueOf(String s, int radix) throws NumberFormatException {
    return Long.valueOf(parseLong(s, radix));
  }

  /**
   * Returns a {@code Long} object holding the value
   * of the specified {@code String}. The argument is
   * interpreted as representing a signed decimal {@code long},
   * exactly as if the argument were given to the {@link
   * #parseLong(java.lang.String)} method. The result is a
   * {@code Long} object that represents the integer value
   * specified by the string.
   *
   * <p>In other words, this method returns a {@code Long} object
   * equal to the value of:
   *
   * <blockquote>
   * {@code new Long(Long.parseLong(s))}
   * </blockquote>
   *
   * @param s the string to be parsed.
   * @return a {@code Long} object holding the value represented by the string argument.
   * @throws NumberFormatException If the string cannot be parsed as a {@code long}.
   */
  public static Long valueOf(String s) throws NumberFormatException {
    return Long.valueOf(parseLong(s, 10));
  }

  private static class LongCache {

    private LongCache() {
    }

    static final Long cache[] = new Long[-(-128) + 127 + 1];

    static {
      for (int i = 0; i < cache.length; i++) {
        cache[i] = new Long(i - 128);
      }
    }
  }

  /**
   * Returns a {@code Long} instance representing the specified
   * {@code long} value.
   * If a new {@code Long} instance is not required, this method
   * should generally be used in preference to the constructor
   * {@link #Long(long)}, as this method is likely to yield
   * significantly better space and time performance by caching
   * frequently requested values.
   *
   * Note that unlike the {@linkplain Integer#valueOf(int)
   * corresponding method} in the {@code Integer} class, this method
   * is <em>not</em> required to cache values within a particular
   * range.
   *
   * @param l a long value.
   * @return a {@code Long} instance representing {@code l}.
   * @since 1.5
   */
  public static Long valueOf(long l) {
    final int offset = 128;
    if (l >= -128 && l <= 127) { // will cache
      return LongCache.cache[(int) l + offset];
    }
    return new Long(l);
  }

  /**
   * Decodes a {@code String} into a {@code Long}.
   * Accepts decimal, hexadecimal, and octal numbers given by the
   * following grammar:
   *
   * <blockquote>
   * <dl>
   * <dt><i>DecodableString:</i>
   * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
   *
   * <dt><i>Sign:</i>
   * <dd>{@code -}
   * <dd>{@code +}
   * </dl>
   * </blockquote>
   *
   * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
   * are as defined in section 3.10.1 of
   * <cite>The Java&trade; Language Specification</cite>,
   * except that underscores are not accepted between digits.
   *
   * <p>The sequence of characters following an optional
   * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
   * "{@code #}", or leading zero) is parsed as by the {@code
   * Long.parseLong} method with the indicated radix (10, 16, or 8).
   * This sequence of characters must represent a positive value or
   * a {@link NumberFormatException} will be thrown.  The result is
   * negated if first character of the specified {@code String} is
   * the minus sign.  No whitespace characters are permitted in the
   * {@code String}.
   *
   * @param nm the {@code String} to decode.
   * @return a {@code Long} object holding the {@code long} value represented by {@code nm}
   * @throws NumberFormatException if the {@code String} does not contain a parsable {@code long}.
   * @see java.lang.Long#parseLong(String, int)
   * @since 1.2
   */
  public static Long decode(String nm) throws NumberFormatException {
    int radix = 10;
    int index = 0;
    boolean negative = false;
    Long result;

    if (nm.length() == 0) {
      throw new NumberFormatException("Zero length string");
    }
    char firstChar = nm.charAt(0);
    // Handle sign, if present
    if (firstChar == '-') {
      negative = true;
      index++;
    } else if (firstChar == '+') {
      index++;
    }

    // Handle radix specifier, if present
    if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
      index += 2;
      radix = 16;
    } else if (nm.startsWith("#", index)) {
      index++;
      radix = 16;
    } else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
      index++;
      radix = 8;
    }

    if (nm.startsWith("-", index) || nm.startsWith("+", index)) {
      throw new NumberFormatException("Sign character in wrong position");
    }

    try {
      result = Long.valueOf(nm.substring(index), radix);
      result = negative ? Long.valueOf(-result.longValue()) : result;
    } catch (NumberFormatException e) {
      // If number is Long.MIN_VALUE, we'll end up here. The next line
      // handles this case, and causes any genuine format error to be
      // rethrown.
      String constant = negative ? ("-" + nm.substring(index))
          : nm.substring(index);
      result = Long.valueOf(constant, radix);
    }
    return result;
  }

  /**
   * The value of the {@code Long}.
   *
   * @serial
   */
  private final long value;

  /**
   * Constructs a newly allocated {@code Long} object that
   * represents the specified {@code long} argument.
   *
   * @param value the value to be represented by the {@code Long} object.
   */
  public Long(long value) {
    this.value = value;
  }

  /**
   * Constructs a newly allocated {@code Long} object that
   * represents the {@code long} value indicated by the
   * {@code String} parameter. The string is converted to a
   * {@code long} value in exactly the manner used by the
   * {@code parseLong} method for radix 10.
   *
   * @param s the {@code String} to be converted to a {@code Long}.
   * @throws NumberFormatException if the {@code String} does not contain a parsable {@code long}.
   * @see java.lang.Long#parseLong(java.lang.String, int)
   */
  public Long(String s) throws NumberFormatException {
    this.value = parseLong(s, 10);
  }

  /**
   * Returns the value of this {@code Long} as a {@code byte} after
   * a narrowing primitive conversion.
   *
   * @jls 5.1.3 Narrowing Primitive Conversions
   */
  public byte byteValue() {
    return (byte) value;
  }

  /**
   * Returns the value of this {@code Long} as a {@code short} after
   * a narrowing primitive conversion.
   *
   * @jls 5.1.3 Narrowing Primitive Conversions
   */
  public short shortValue() {
    return (short) value;
  }

  /**
   * Returns the value of this {@code Long} as an {@code int} after
   * a narrowing primitive conversion.
   *
   * @jls 5.1.3 Narrowing Primitive Conversions
   */
  public int intValue() {
    return (int) value;
  }

  /**
   * Returns the value of this {@code Long} as a
   * {@code long} value.
   */
  public long longValue() {
    return value;
  }

  /**
   * Returns the value of this {@code Long} as a {@code float} after
   * a widening primitive conversion.
   *
   * @jls 5.1.2 Widening Primitive Conversions
   */
  public float floatValue() {
    return (float) value;
  }

  /**
   * Returns the value of this {@code Long} as a {@code double}
   * after a widening primitive conversion.
   *
   * @jls 5.1.2 Widening Primitive Conversions
   */
  public double doubleValue() {
    return (double) value;
  }

  /**
   * Returns a {@code String} object representing this
   * {@code Long}'s value.  The value is converted to signed
   * decimal representation and returned as a string, exactly as if
   * the {@code long} value were given as an argument to the
   * {@link java.lang.Long#toString(long)} method.
   *
   * @return a string representation of the value of this object in base&nbsp;10.
   */
  public String toString() {
    return toString(value);
  }

  /**
   * Returns a hash code for this {@code Long}. The result is
   * the exclusive OR of the two halves of the primitive
   * {@code long} value held by this {@code Long}
   * object. That is, the hashcode is the value of the expression:
   *
   * <blockquote>
   * {@code (int)(this.longValue()^(this.longValue()>>>32))}
   * </blockquote>
   *
   * @return a hash code value for this object.
   */
  @Override
  public int hashCode() {
    return Long.hashCode(value);
  }

  /**
   * Returns a hash code for a {@code long} value; compatible with
   * {@code Long.hashCode()}.
   *
   * @param value the value to hash
   * @return a hash code value for a {@code long} value.
   * @since 1.8
   */
  public static int hashCode(long value) {
    return (int) (value ^ (value >>> 32));
  }

  /**
   * Compares this object to the specified object.  The result is
   * {@code true} if and only if the argument is not
   * {@code null} and is a {@code Long} object that
   * contains the same {@code long} value as this object.
   *
   * @param obj the object to compare with.
   * @return {@code true} if the objects are the same; {@code false} otherwise.
   */
  public boolean equals(Object obj) {
    if (obj instanceof Long) {
      return value == ((Long) obj).longValue();
    }
    return false;
  }

  /**
   * Determines the {@code long} value of the system property
   * with the specified name.
   *
   * <p>The first argument is treated as the name of a system
   * property.  System properties are accessible through the {@link
   * java.lang.System#getProperty(java.lang.String)} method. The
   * string value of this property is then interpreted as a {@code
   * long} value using the grammar supported by {@link Long#decode decode}
   * and a {@code Long} object representing this value is returned.
   *
   * <p>If there is no property with the specified name, if the
   * specified name is empty or {@code null}, or if the property
   * does not have the correct numeric format, then {@code null} is
   * returned.
   *
   * <p>In other words, this method returns a {@code Long} object
   * equal to the value of:
   *
   * <blockquote>
   * {@code getLong(nm, null)}
   * </blockquote>
   *
   * @param nm property name.
   * @return the {@code Long} value of the property.
   * @throws SecurityException for the same reasons as {@link System#getProperty(String)
   * System.getProperty}
   * @see java.lang.System#getProperty(java.lang.String)
   * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
   */
  public static Long getLong(String nm) {
    return getLong(nm, null);
  }

  /**
   * Determines the {@code long} value of the system property
   * with the specified name.
   *
   * <p>The first argument is treated as the name of a system
   * property.  System properties are accessible through the {@link
   * java.lang.System#getProperty(java.lang.String)} method. The
   * string value of this property is then interpreted as a {@code
   * long} value using the grammar supported by {@link Long#decode decode}
   * and a {@code Long} object representing this value is returned.
   *
   * <p>The second argument is the default value. A {@code Long} object
   * that represents the value of the second argument is returned if there
   * is no property of the specified name, if the property does not have
   * the correct numeric format, or if the specified name is empty or null.
   *
   * <p>In other words, this method returns a {@code Long} object equal
   * to the value of:
   *
   * <blockquote>
   * {@code getLong(nm, new Long(val))}
   * </blockquote>
   *
   * but in practice it may be implemented in a manner such as:
   *
   * <blockquote><pre>
   * Long result = getLong(nm, null);
   * return (result == null) ? new Long(val) : result;
   * </pre></blockquote>
   *
   * to avoid the unnecessary allocation of a {@code Long} object when
   * the default value is not needed.
   *
   * @param nm property name.
   * @param val default value.
   * @return the {@code Long} value of the property.
   * @throws SecurityException for the same reasons as {@link System#getProperty(String)
   * System.getProperty}
   * @see java.lang.System#getProperty(java.lang.String)
   * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
   */
  public static Long getLong(String nm, long val) {
    Long result = Long.getLong(nm, null);
    return (result == null) ? Long.valueOf(val) : result;
  }

  /**
   * Returns the {@code long} value of the system property with
   * the specified name.  The first argument is treated as the name
   * of a system property.  System properties are accessible through
   * the {@link java.lang.System#getProperty(java.lang.String)}
   * method. The string value of this property is then interpreted
   * as a {@code long} value, as per the
   * {@link Long#decode decode} method, and a {@code Long} object
   * representing this value is returned; in summary:
   *
   * <ul>
   * <li>If the property value begins with the two ASCII characters
   * {@code 0x} or the ASCII character {@code #}, not followed by
   * a minus sign, then the rest of it is parsed as a hexadecimal integer
   * exactly as for the method {@link #valueOf(java.lang.String, int)}
   * with radix 16.
   * <li>If the property value begins with the ASCII character
   * {@code 0} followed by another character, it is parsed as
   * an octal integer exactly as by the method {@link
   * #valueOf(java.lang.String, int)} with radix 8.
   * <li>Otherwise the property value is parsed as a decimal
   * integer exactly as by the method
   * {@link #valueOf(java.lang.String, int)} with radix 10.
   * </ul>
   *
   * <p>Note that, in every case, neither {@code L}
   * ({@code '\u005Cu004C'}) nor {@code l}
   * ({@code '\u005Cu006C'}) is permitted to appear at the end
   * of the property value as a type indicator, as would be
   * permitted in Java programming language source code.
   *
   * <p>The second argument is the default value. The default value is
   * returned if there is no property of the specified name, if the
   * property does not have the correct numeric format, or if the
   * specified name is empty or {@code null}.
   *
   * @param nm property name.
   * @param val default value.
   * @return the {@code Long} value of the property.
   * @throws SecurityException for the same reasons as {@link System#getProperty(String)
   * System.getProperty}
   * @see System#getProperty(java.lang.String)
   * @see System#getProperty(java.lang.String, java.lang.String)
   */
  public static Long getLong(String nm, Long val) {
    String v = null;
    try {
      v = System.getProperty(nm);
    } catch (IllegalArgumentException | NullPointerException e) {
    }
    if (v != null) {
      try {
        return Long.decode(v);
      } catch (NumberFormatException e) {
      }
    }
    return val;
  }

  /**
   * Compares two {@code Long} objects numerically.
   *
   * @param anotherLong the {@code Long} to be compared.
   * @return the value {@code 0} if this {@code Long} is equal to the argument {@code Long}; a value
   * less than {@code 0} if this {@code Long} is numerically less than the argument {@code Long};
   * and a value greater than {@code 0} if this {@code Long} is numerically greater than the
   * argument {@code Long} (signed comparison).
   * @since 1.2
   */
  public int compareTo(Long anotherLong) {
    return compare(this.value, anotherLong.value);
  }

  /**
   * Compares two {@code long} values numerically.
   * The value returned is identical to what would be returned by:
   * <pre>
   *    Long.valueOf(x).compareTo(Long.valueOf(y))
   * </pre>
   *
   * @param x the first {@code long} to compare
   * @param y the second {@code long} to compare
   * @return the value {@code 0} if {@code x == y}; a value less than {@code 0} if {@code x < y};
   * and a value greater than {@code 0} if {@code x > y}
   * @since 1.7
   */
  public static int compare(long x, long y) {
    return (x < y) ? -1 : ((x == y) ? 0 : 1);
  }

  /**
   * Compares two {@code long} values numerically treating the values
   * as unsigned.
   *
   * @param x the first {@code long} to compare
   * @param y the second {@code long} to compare
   * @return the value {@code 0} if {@code x == y}; a value less than {@code 0} if {@code x < y} as
   * unsigned values; and a value greater than {@code 0} if {@code x > y} as unsigned values
   * @since 1.8
   */
  public static int compareUnsigned(long x, long y) {
    return compare(x + MIN_VALUE, y + MIN_VALUE);
  }


  /**
   * Returns the unsigned quotient of dividing the first argument by
   * the second where each argument and the result is interpreted as
   * an unsigned value.
   *
   * <p>Note that in two's complement arithmetic, the three other
   * basic arithmetic operations of add, subtract, and multiply are
   * bit-wise identical if the two operands are regarded as both
   * being signed or both being unsigned.  Therefore separate {@code
   * addUnsigned}, etc. methods are not provided.
   *
   * @param dividend the value to be divided
   * @param divisor the value doing the dividing
   * @return the unsigned quotient of the first argument divided by the second argument
   * @see #remainderUnsigned
   * @since 1.8
   */
  public static long divideUnsigned(long dividend, long divisor) {
    if (divisor < 0L) { // signed comparison
      // Answer must be 0 or 1 depending on relative magnitude
      // of dividend and divisor.
      return (compareUnsigned(dividend, divisor)) < 0 ? 0L : 1L;
    }

    if (dividend > 0) //  Both inputs non-negative
    {
      return dividend / divisor;
    } else {
            /*
             * For simple code, leveraging BigInteger.  Longer and faster
             * code written directly in terms of operations on longs is
             * possible; see "Hacker's Delight" for divide and remainder
             * algorithms.
             */
      return toUnsignedBigInteger(dividend).
          divide(toUnsignedBigInteger(divisor)).longValue();
    }
  }

  /**
   * Returns the unsigned remainder from dividing the first argument
   * by the second where each argument and the result is interpreted
   * as an unsigned value.
   *
   * @param dividend the value to be divided
   * @param divisor the value doing the dividing
   * @return the unsigned remainder of the first argument divided by the second argument
   * @see #divideUnsigned
   * @since 1.8
   */
  public static long remainderUnsigned(long dividend, long divisor) {
    if (dividend > 0 && divisor > 0) { // signed comparisons
      return dividend % divisor;
    } else {
      if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
      {
        return dividend;
      } else {
        return toUnsignedBigInteger(dividend).
            remainder(toUnsignedBigInteger(divisor)).longValue();
      }
    }
  }

  // Bit Twiddling

  /**
   * The number of bits used to represent a {@code long} value in two's
   * complement binary form.
   *
   * @since 1.5
   */
  @Native
  public static final int SIZE = 64;

  /**
   * The number of bytes used to represent a {@code long} value in two's
   * complement binary form.
   *
   * @since 1.8
   */
  public static final int BYTES = SIZE / Byte.SIZE;

  /**
   * Returns a {@code long} value with at most a single one-bit, in the
   * position of the highest-order ("leftmost") one-bit in the specified
   * {@code long} value.  Returns zero if the specified value has no
   * one-bits in its two's complement binary representation, that is, if it
   * is equal to zero.
   *
   * @param i the value whose highest one bit is to be computed
   * @return a {@code long} value with a single one-bit, in the position of the highest-order
   * one-bit in the specified value, or zero if the specified value is itself equal to zero.
   * @since 1.5
   */
  public static long highestOneBit(long i) {
    // HD, Figure 3-1
    i |= (i >> 1);
    i |= (i >> 2);
    i |= (i >> 4);
    i |= (i >> 8);
    i |= (i >> 16);
    i |= (i >> 32);
    return i - (i >>> 1);
  }

  /**
   * Returns a {@code long} value with at most a single one-bit, in the
   * position of the lowest-order ("rightmost") one-bit in the specified
   * {@code long} value.  Returns zero if the specified value has no
   * one-bits in its two's complement binary representation, that is, if it
   * is equal to zero.
   *
   * @param i the value whose lowest one bit is to be computed
   * @return a {@code long} value with a single one-bit, in the position of the lowest-order one-bit
   * in the specified value, or zero if the specified value is itself equal to zero.
   * @since 1.5
   */
  public static long lowestOneBit(long i) {
    // HD, Section 2-1
    return i & -i;
  }

  /**
   * Returns the number of zero bits preceding the highest-order
   * ("leftmost") one-bit in the two's complement binary representation
   * of the specified {@code long} value.  Returns 64 if the
   * specified value has no one-bits in its two's complement representation,
   * in other words if it is equal to zero.
   *
   * <p>Note that this method is closely related to the logarithm base 2.
   * For all positive {@code long} values x:
   * <ul>
   * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
   * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
   * </ul>
   *
   * @param i the value whose number of leading zeros is to be computed
   * @return the number of zero bits preceding the highest-order ("leftmost") one-bit in the two's
   * complement binary representation of the specified {@code long} value, or 64 if the value is
   * equal to zero.
   * @since 1.5
   */
  public static int numberOfLeadingZeros(long i) {
    // HD, Figure 5-6
    if (i == 0) {
      return 64;
    }
    int n = 1;
    int x = (int) (i >>> 32);
    if (x == 0) {
      n += 32;
      x = (int) i;
    }
    if (x >>> 16 == 0) {
      n += 16;
      x <<= 16;
    }
    if (x >>> 24 == 0) {
      n += 8;
      x <<= 8;
    }
    if (x >>> 28 == 0) {
      n += 4;
      x <<= 4;
    }
    if (x >>> 30 == 0) {
      n += 2;
      x <<= 2;
    }
    n -= x >>> 31;
    return n;
  }

  /**
   * Returns the number of zero bits following the lowest-order ("rightmost")
   * one-bit in the two's complement binary representation of the specified
   * {@code long} value.  Returns 64 if the specified value has no
   * one-bits in its two's complement representation, in other words if it is
   * equal to zero.
   *
   * @param i the value whose number of trailing zeros is to be computed
   * @return the number of zero bits following the lowest-order ("rightmost") one-bit in the two's
   * complement binary representation of the specified {@code long} value, or 64 if the value is
   * equal to zero.
   * @since 1.5
   */
  public static int numberOfTrailingZeros(long i) {
    // HD, Figure 5-14
    int x, y;
    if (i == 0) {
      return 64;
    }
    int n = 63;
    y = (int) i;
    if (y != 0) {
      n = n - 32;
      x = y;
    } else {
      x = (int) (i >>> 32);
    }
    y = x << 16;
    if (y != 0) {
      n = n - 16;
      x = y;
    }
    y = x << 8;
    if (y != 0) {
      n = n - 8;
      x = y;
    }
    y = x << 4;
    if (y != 0) {
      n = n - 4;
      x = y;
    }
    y = x << 2;
    if (y != 0) {
      n = n - 2;
      x = y;
    }
    return n - ((x << 1) >>> 31);
  }

  /**
   * Returns the number of one-bits in the two's complement binary
   * representation of the specified {@code long} value.  This function is
   * sometimes referred to as the <i>population count</i>.
   *
   * @param i the value whose bits are to be counted
   * @return the number of one-bits in the two's complement binary representation of the specified
   * {@code long} value.
   * @since 1.5
   */
  public static int bitCount(long i) {
    // HD, Figure 5-14
    i = i - ((i >>> 1) & 0x5555555555555555L);
    i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
    i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
    i = i + (i >>> 8);
    i = i + (i >>> 16);
    i = i + (i >>> 32);
    return (int) i & 0x7f;
  }

  /**
   * Returns the value obtained by rotating the two's complement binary
   * representation of the specified {@code long} value left by the
   * specified number of bits.  (Bits shifted out of the left hand, or
   * high-order, side reenter on the right, or low-order.)
   *
   * <p>Note that left rotation with a negative distance is equivalent to
   * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
   * distance)}.  Note also that rotation by any multiple of 64 is a
   * no-op, so all but the last six bits of the rotation distance can be
   * ignored, even if the distance is negative: {@code rotateLeft(val,
   * distance) == rotateLeft(val, distance & 0x3F)}.
   *
   * @param i the value whose bits are to be rotated left
   * @param distance the number of bit positions to rotate left
   * @return the value obtained by rotating the two's complement binary representation of the
   * specified {@code long} value left by the specified number of bits.
   * @since 1.5
   */
  public static long rotateLeft(long i, int distance) {
    return (i << distance) | (i >>> -distance);
  }

  /**
   * Returns the value obtained by rotating the two's complement binary
   * representation of the specified {@code long} value right by the
   * specified number of bits.  (Bits shifted out of the right hand, or
   * low-order, side reenter on the left, or high-order.)
   *
   * <p>Note that right rotation with a negative distance is equivalent to
   * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
   * distance)}.  Note also that rotation by any multiple of 64 is a
   * no-op, so all but the last six bits of the rotation distance can be
   * ignored, even if the distance is negative: {@code rotateRight(val,
   * distance) == rotateRight(val, distance & 0x3F)}.
   *
   * @param i the value whose bits are to be rotated right
   * @param distance the number of bit positions to rotate right
   * @return the value obtained by rotating the two's complement binary representation of the
   * specified {@code long} value right by the specified number of bits.
   * @since 1.5
   */
  public static long rotateRight(long i, int distance) {
    return (i >>> distance) | (i << -distance);
  }

  /**
   * Returns the value obtained by reversing the order of the bits in the
   * two's complement binary representation of the specified {@code long}
   * value.
   *
   * @param i the value to be reversed
   * @return the value obtained by reversing order of the bits in the specified {@code long} value.
   * @since 1.5
   */
  public static long reverse(long i) {
    // HD, Figure 7-1
    i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
    i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
    i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
    i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
    i = (i << 48) | ((i & 0xffff0000L) << 16) |
        ((i >>> 16) & 0xffff0000L) | (i >>> 48);
    return i;
  }

  /**
   * Returns the signum function of the specified {@code long} value.  (The
   * return value is -1 if the specified value is negative; 0 if the
   * specified value is zero; and 1 if the specified value is positive.)
   *
   * @param i the value whose signum is to be computed
   * @return the signum function of the specified {@code long} value.
   * @since 1.5
   */
  public static int signum(long i) {
    // HD, Section 2-7
    return (int) ((i >> 63) | (-i >>> 63));
  }

  /**
   * Returns the value obtained by reversing the order of the bytes in the
   * two's complement representation of the specified {@code long} value.
   *
   * @param i the value whose bytes are to be reversed
   * @return the value obtained by reversing the bytes in the specified {@code long} value.
   * @since 1.5
   */
  public static long reverseBytes(long i) {
    i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
    return (i << 48) | ((i & 0xffff0000L) << 16) |
        ((i >>> 16) & 0xffff0000L) | (i >>> 48);
  }

  /**
   * Adds two {@code long} values together as per the + operator.
   *
   * @param a the first operand
   * @param b the second operand
   * @return the sum of {@code a} and {@code b}
   * @see java.util.function.BinaryOperator
   * @since 1.8
   */
  public static long sum(long a, long b) {
    return a + b;
  }

  /**
   * Returns the greater of two {@code long} values
   * as if by calling {@link Math#max(long, long) Math.max}.
   *
   * @param a the first operand
   * @param b the second operand
   * @return the greater of {@code a} and {@code b}
   * @see java.util.function.BinaryOperator
   * @since 1.8
   */
  public static long max(long a, long b) {
    return Math.max(a, b);
  }

  /**
   * Returns the smaller of two {@code long} values
   * as if by calling {@link Math#min(long, long) Math.min}.
   *
   * @param a the first operand
   * @param b the second operand
   * @return the smaller of {@code a} and {@code b}
   * @see java.util.function.BinaryOperator
   * @since 1.8
   */
  public static long min(long a, long b) {
    return Math.min(a, b);
  }

  /**
   * use serialVersionUID from JDK 1.0.2 for interoperability
   */
  @Native
  private static final long serialVersionUID = 4290774380558885855L;
}
